RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-05-04_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 21.2695 0.785535
2 to 25 15.61 18.6412 0.650486
3 to 26 15.74 20.8709 0.767880
4 to 27 15.80 9.7997 0.088202
5 to 28 15.83 19.2160 0.683725
6 to 29 15.67 26.4761 0.933788
7 to 30 15.75 16.1230 0.484870
8 to 31 15.82 24.6375 0.896877
9 to 32 15.76 14.7834 0.388922
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.298498
Tough bday spacings test for dh-ranFile-2017-05-04_20:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 10 34 65 110 104 85 52 25 11 4 0
(O-E)^2/E 0.1 0.2 0.9 1.6 0.4 0.6 0.0 0.8 1.0 1.0 4.1
Birthday Spacings: Sum(O-E)^2/E= 10.640, p= 0.614
RESULTS OF GCD FOR dh-ranFile-2017-05-04_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.679008
p-value, dist. of gcd's: 0.231819
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-05-04_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.835 0.259 0.231 0.883 0.530 0.182 0.966 0.781
Bits 8 to 15---> 0.805 0.081 0.332 0.671 0.786 0.780 0.731 0.021
Bits 16 to 23---> 0.292 0.684 0.583 0.334 0.950 0.357 0.602 0.532
Bits 24 to 31---> 0.915 0.043 0.893 0.911 0.154 0.605 0.968 0.695
KS test for the above 32 p values: 0.782
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-05-04_20:31,
p-values for 5 runs: 0.6800, 0.5253, 0.4246, 0.6323, 0.2664
Rank test for binary matrices (31x31) for dh-ranFile-2017-05-04_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5120 5134.0 0.038 0.787
r= 30 23019 23103.0 0.306 1.093
r= 31 11637 11551.5 0.632 1.725
chi-square = 1.725 with df = 3; p-value = 0.369
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-05-04_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5123 5134.0 0.024 0.079
r= 31 23009 23103.0 0.383 0.462
r= 32 11660 11551.5 1.019 1.480
chi-square = 1.480 with df = 3; p-value = 0.313
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-05-04_20:31
b-rank test for bits 1 to 8, p=0.65212
b-rank test for bits 2 to 9, p=0.67736
b-rank test for bits 3 to 10, p=0.80845
b-rank test for bits 4 to 11, p=0.40914
b-rank test for bits 5 to 12, p=0.06347
b-rank test for bits 6 to 13, p=0.18993
b-rank test for bits 7 to 14, p=0.97395
b-rank test for bits 8 to 15, p=0.98900
b-rank test for bits 9 to 16, p=0.70368
b-rank test for bits 10 to 17, p=0.68373
b-rank test for bits 11 to 18, p=0.59006
b-rank test for bits 12 to 19, p=0.47731
b-rank test for bits 13 to 20, p=0.01814
b-rank test for bits 14 to 21, p=0.95042
b-rank test for bits 15 to 22, p=0.46593
b-rank test for bits 16 to 23, p=0.80004
b-rank test for bits 17 to 24, p=0.88411
b-rank test for bits 18 to 25, p=0.01784
b-rank test for bits 19 to 26, p=0.33559
b-rank test for bits 20 to 27, p=0.41944
b-rank test for bits 21 to 28, p=0.29529
b-rank test for bits 22 to 29, p=0.31916
b-rank test for bits 23 to 30, p=0.69699
b-rank test for bits 24 to 31, p=0.60041
b-rank test for bits 25 to 32, p=0.75901
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.539748
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-05-04_20:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141530 -0.89 0.187732
2 142413 1.18 0.880362
3 142283 0.87 0.808685
4 141326 -1.36 0.086454
5 141718 -0.45 0.327426
6 142270 0.84 0.800298
7 142550 1.50 0.932789
8 141184 -1.69 0.045067
9 141291 -1.44 0.074272
10 142106 0.46 0.677066
11 141526 -0.90 0.185225
12 141980 0.17 0.565574
13 142227 0.74 0.771023
14 142081 0.40 0.655826
15 142261 0.82 0.794364
16 141796 -0.26 0.395586
17 141904 -0.01 0.495032
18 142802 2.09 0.981496
19 142119 0.49 0.687892
20 141943 0.08 0.531352
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-05-04_20:31
Bits used No. missing words z-score p-value
23 to 32 142039 0.4471 0.672612
22 to 31 141283 -2.1598 0.015396
21 to 30 142635 2.5023 0.993831
20 to 29 142338 1.4782 0.930319
19 to 28 141649 -0.8977 0.184676
18 to 27 142116 0.7127 0.761970
17 to 26 141940 0.1058 0.542113
16 to 25 141603 -1.0563 0.145413
15 to 24 141763 -0.5046 0.306925
14 to 23 142316 1.4023 0.919589
13 to 22 141724 -0.6391 0.261389
12 to 21 141662 -0.8529 0.196868
11 to 20 141943 0.1161 0.546215
10 to 19 141557 -1.2149 0.112196
9 to 18 141591 -1.0977 0.136170
8 to 17 142035 0.4333 0.667618
7 to 16 142187 0.9575 0.830838
6 to 15 142125 0.7437 0.771468
5 to 14 141211 -2.4080 0.008019
4 to 13 142034 0.4299 0.666365
3 to 12 141754 -0.5356 0.296110
2 to 11 142029 0.4127 0.660070
1 to 10 141821 -0.3046 0.380341
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-05-04_20:31
Bits used No. missing words z-score p-value
28 to 32 141917 0.0260 0.510371
27 to 31 141550 -1.2181 0.111599
26 to 30 141651 -0.8757 0.190598
25 to 29 142039 0.4396 0.669872
24 to 28 141789 -0.4079 0.341674
23 to 27 142069 0.5413 0.705834
22 to 26 142078 0.5718 0.716259
21 to 25 142244 1.1345 0.871702
20 to 24 141572 -1.1435 0.126417
19 to 23 142017 0.3650 0.642438
18 to 22 141721 -0.6384 0.261605
17 to 21 141925 0.0531 0.521181
16 to 20 141439 -1.5943 0.055430
15 to 19 141624 -0.9672 0.166717
14 to 18 142057 0.5006 0.691665
13 to 17 141726 -0.6215 0.267149
12 to 16 142019 0.3718 0.644965
11 to 15 141541 -1.2486 0.105910
10 to 14 142102 0.6531 0.743160
9 to 13 142206 1.0057 0.842711
8 to 12 141424 -1.6452 0.049966
7 to 11 142319 1.3887 0.917540
6 to 10 141080 -2.8113 0.002467
5 to 9 141646 -0.8926 0.186024
4 to 8 142209 1.0158 0.845145
3 to 7 142550 2.1718 0.985063
2 to 6 141960 0.1718 0.568188
1 to 5 141580 -1.1164 0.132131
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-05-04_20:31
Bits used No. missing words z-score p-value
31 to 32 141757 -0.4494 0.326589
30 to 31 142000 0.2675 0.605444
29 to 30 141295 -1.8122 0.034979
28 to 29 142553 1.8987 0.971200
27 to 28 142315 1.1967 0.884282
26 to 27 141632 -0.8181 0.206655
25 to 26 142387 1.4091 0.920591
24 to 25 142633 2.1347 0.983608
23 to 24 141914 0.0138 0.505496
22 to 23 141952 0.1259 0.550083
21 to 22 141631 -0.8210 0.205814
20 to 21 142373 1.3678 0.914306
19 to 20 142128 0.6450 0.740551
18 to 19 141789 -0.3550 0.361311
17 to 18 142093 0.5418 0.706022
16 to 17 141984 0.2203 0.587168
15 to 16 141889 -0.0600 0.476090
14 to 15 142168 0.7630 0.777280
13 to 14 142209 0.8840 0.811647
12 to 13 141053 -2.5260 0.005768
11 to 12 142128 0.6450 0.740551
10 to 11 141369 -1.5939 0.055480
9 to 10 141990 0.2380 0.594046
8 to 9 142544 1.8722 0.969409
7 to 8 142311 1.1849 0.881965
6 to 7 141729 -0.5319 0.297381
5 to 6 141641 -0.7915 0.214316
4 to 5 141975 0.1937 0.576801
3 to 4 141942 0.0964 0.538387
2 to 3 142365 1.3442 0.910552
1 to 2 141993 0.2468 0.597474
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-05-04_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2434.19 -0.931 0.176005
Test results for specific bytes for dh-ranFile-2017-05-04_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2426.71 -1.036 0.150003
2 to 9 2525.94 0.367 0.643143
3 to 10 2417.44 -1.168 0.121500
4 to 11 2493.20 -0.096 0.461676
5 to 12 2511.99 0.170 0.567309
6 to 13 2577.16 1.091 0.862423
7 to 14 2366.21 -1.892 0.029244
8 to 15 2596.04 1.358 0.912804
9 to 16 2540.85 0.578 0.718269
10 to 17 2428.83 -1.007 0.157074
11 to 18 2482.83 -0.243 0.404065
12 to 19 2530.38 0.430 0.666293
13 to 20 2454.38 -0.645 0.259418
14 to 21 2432.49 -0.955 0.169864
15 to 22 2526.19 0.370 0.644467
16 to 23 2514.87 0.210 0.583292
17 to 24 2497.97 -0.029 0.488554
18 to 25 2417.91 -1.161 0.122838
19 to 26 2520.59 0.291 0.614547
20 to 27 2614.04 1.613 0.946607
21 to 28 2496.61 -0.048 0.480894
22 to 29 2513.78 0.195 0.577231
23 to 30 2583.16 1.176 0.880208
24 to 31 2471.15 -0.408 0.341655
25 to 32 2536.26 0.513 0.695944
CDPARK for dh-ranFile-2017-05-04_20:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3524 0.0457 0.518210
3557 1.5525 0.939730
3523 0.0000 0.500000
3521 -0.0913 0.463617
3534 0.5023 0.692266
3497 -1.1872 0.117571
3539 0.7306 0.767486
3564 1.8721 0.969407
3532 0.4110 0.659449
3523 0.0000 0.500000
Square side=100, avg. no. parked=3531.40 sample std.=18.08
p-value of the KSTEST for those 10 p-values: 0.299173
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-05-04_20:31
0.4844,0.6962,0.0991,0.5991,0.1102,0.0447,0.4700,0.4473,0.3238,0.2752,
The KS test for those 10 p-values: 0.169672
The 3DSPHERES test for dh-ranFile-2017-05-04_20:31
sample no r^3 equiv. uni.
1 27.128 0.595159
2 69.885 0.902656
3 40.862 0.743867
4 46.394 0.787003
5 14.890 0.391249
6 20.794 0.499987
7 6.548 0.196087
8 32.022 0.656101
9 46.298 0.786319
10 8.461 0.245758
11 19.381 0.475885
12 20.737 0.499036
13 11.722 0.323446
14 75.082 0.918139
15 61.189 0.869925
16 36.893 0.707641
17 42.975 0.761285
18 2.067 0.066576
19 13.001 0.351674
20 151.688 0.993631
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.305246
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-05-04_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 1.3 -1.9 -1.0 0.5
0.0 0.0 0.2 2.0 -0.5 0.3
-0.1 -0.3 0.4 0.1 0.2 0.7
0.6 -0.5 0.5 -0.4 0.6 0.2
-1.9 0.2 0.5 -2.0 -1.3 1.0
-2.2 -0.7 -1.9 -0.5 -0.6 -1.2
-1.2 -0.7 0.9 2.6 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:45.565482
z-score=0.389026, p-value=0.673953
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-05-04_20:31
Test no p-value
1 0.950914
2 0.754302
3 0.138897
4 0.404092
5 0.646046
6 0.026433
7 0.699099
8 0.049488
9 0.305197
10 0.508288
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.832882
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-05-04_20:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66372 1.30 66735 0.07
3 25000.00 25270 2.92 24852 0.88
4 6666.67 6626 0.25 6710 0.28
5 1388.89 1463 3.95 1407 0.24
6 238.10 229 0.35 256 1.35
7 34.72 36 0.05 30 0.64
8 4.96 3 0.77 9 3.29
p=0.85699 p=0.65470
Number of rngs required: 689660, p-value: 0.929
RESULTS OF CRAPS TEST for dh-ranFile-2017-05-04_20:31
No. of wins: Observed Expected
98603 98585.9
z-score= 0.077, pvalue=0.53056
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66528 66666.7 0.288 0.288
2 37827 37654.3 0.792 1.080
3 27173 26954.7 1.767 2.848
4 19070 19313.5 3.069 5.917
5 13835 13851.4 0.019 5.936
6 10032 9943.5 0.787 6.723
7 7160 7145.0 0.031 6.755
8 5165 5139.1 0.131 6.885
9 3715 3699.9 0.062 6.947
10 2628 2666.3 0.550 7.497
11 1910 1923.3 0.092 7.590
12 1389 1388.7 0.000 7.590
13 997 1003.7 0.045 7.635
14 716 726.1 0.142 7.776
15 495 525.8 1.808 9.585
16 344 381.2 3.621 13.206
17 266 276.5 0.402 13.607
18 206 200.8 0.133 13.740
19 148 146.0 0.028 13.768
20 96 106.2 0.982 14.751
21 300 287.1 0.578 15.329
Chisq= 15.33 for 20 degrees of freedom, p= 0.24272
SUMMARY of craptest
p-value for no. of wins: 0.530556
p-value for throws/game: 0.242719
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-05-04_20:31
No. of wins: Observed Expected
98684 98585.9
z-score= 0.439, pvalue=0.66965
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66760 66666.7 0.131 0.131
2 37670 37654.3 0.007 0.137
3 27100 26954.7 0.783 0.920
4 19192 19313.5 0.764 1.684
5 13773 13851.4 0.444 2.128
6 9870 9943.5 0.544 2.672
7 7206 7145.0 0.520 3.192
8 5115 5139.1 0.113 3.305
9 3701 3699.9 0.000 3.305
10 2610 2666.3 1.189 4.494
11 1945 1923.3 0.244 4.738
12 1342 1388.7 1.573 6.311
13 1048 1003.7 1.954 8.265
14 764 726.1 1.974 10.239
15 512 525.8 0.364 10.603
16 349 381.2 2.712 13.315
17 286 276.5 0.324 13.639
18 202 200.8 0.007 13.646
19 146 146.0 0.000 13.646
20 102 106.2 0.167 13.813
21 307 287.1 1.377 15.190
Chisq= 15.19 for 20 degrees of freedom, p= 0.23458
SUMMARY of craptest
p-value for no. of wins: 0.669650
p-value for throws/game: 0.234577
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0025,0.0058,0.0080,0.0154,0.0178,0.0181,0.0210,0.0264,0.0292,0.0350,
0.0431,0.0447,0.0451,0.0495,0.0500,0.0554,0.0555,0.0635,0.0666,0.0743,
0.0810,0.0865,0.0882,0.0991,0.1059,0.1102,0.1116,0.1122,0.1176,0.1215,
0.1228,0.1264,0.1321,0.1362,0.1389,0.1454,0.1500,0.1544,0.1571,0.1667,
0.1697,0.1699,0.1760,0.1824,0.1847,0.1852,0.1860,0.1877,0.1899,0.1906,
0.1961,0.1969,0.2058,0.2067,0.2143,0.2306,0.2318,0.2346,0.2427,0.2458,
0.2592,0.2594,0.2614,0.2616,0.2664,0.2671,0.2752,0.2922,0.2953,0.2961,
0.2974,0.2985,0.2992,0.3052,0.3052,0.3069,0.3132,0.3192,0.3234,0.3238,
0.3266,0.3274,0.3325,0.3341,0.3356,0.3417,0.3417,0.3517,0.3569,0.3613,
0.3687,0.3803,0.3889,0.3912,0.3956,0.4041,0.4041,0.4091,0.4194,0.4246,
0.4473,0.4617,0.4636,0.4659,0.4700,0.4759,0.4761,0.4773,0.4809,0.4844,
0.4849,0.4886,0.4950,0.4990,0.5000,0.5000,0.5000,0.5055,0.5083,0.5104,
0.5182,0.5212,0.5253,0.5300,0.5306,0.5314,0.5315,0.5384,0.5397,0.5421,
0.5462,0.5501,0.5656,0.5673,0.5682,0.5768,0.5772,0.5830,0.5833,0.5872,
0.5901,0.5940,0.5952,0.5975,0.5991,0.6004,0.6017,0.6050,0.6054,0.6137,
0.6145,0.6323,0.6424,0.6431,0.6445,0.6450,0.6460,0.6505,0.6521,0.6547,
0.6558,0.6561,0.6594,0.6601,0.6663,0.6664,0.6676,0.6696,0.6699,0.6709,
0.6726,0.6740,0.6771,0.6774,0.6790,0.6800,0.6837,0.6837,0.6843,0.6879,
0.6917,0.6923,0.6953,0.6959,0.6962,0.6970,0.6991,0.7037,0.7058,0.7060,
0.7076,0.7163,0.7183,0.7312,0.7406,0.7406,0.7432,0.7439,0.7543,0.7590,
0.7613,0.7620,0.7675,0.7679,0.7710,0.7715,0.7773,0.7798,0.7812,0.7818,
0.7855,0.7858,0.7863,0.7870,0.7944,0.8000,0.8003,0.8053,0.8085,0.8087,
0.8116,0.8308,0.8329,0.8353,0.8427,0.8451,0.8570,0.8624,0.8699,0.8717,
0.8802,0.8804,0.8820,0.8826,0.8841,0.8843,0.8930,0.8969,0.9027,0.9106,
0.9110,0.9128,0.9143,0.9153,0.9175,0.9181,0.9196,0.9206,0.9289,0.9303,
0.9328,0.9338,0.9397,0.9466,0.9504,0.9504,0.9509,0.9663,0.9681,0.9694,
0.9694,0.9712,0.9739,0.9815,0.9836,0.9851,0.9890,0.9936,0.9938,
Overall p-value after applying KStest on 269 p-values = 0.134614
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.